Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

TL;DR

The paper addresses the linear stability of tensor perturbations for static, spherically symmetric black holes in Einstein-Gauss-Bonnet gravity in $D>4$. By deriving a Regge-Wheeler-Zerilli master equation and an exact Schrödinger-like potential $V(r)$, the authors provide a precise stability operator for general $D$, $\Lambda$, and $\alpha$. They show that for $\alpha>0$ and $D \neq 6$, all positive-mass black holes are tensor-stable (with $D=5$ and $D\ge 7$ confirming stability, while $D=6$ admits small-mass instabilities); for $\alpha<0$, tensor perturbations can destabilize certain static black holes. These results illuminate the stability landscape of higher-dimensional EGB black holes and have implications for string-inspired gravity theories and AdS/CFT contexts.

Abstract

We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schrödinger-like stability equation. As an immediate application we prove that for $D \neq 6$ and $α>0$, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case $D =6$, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for $α< 0$.

Figures (1)

• Figure 1: The potential $V(r(r^*))$ as a function of $r^*$. Figure 1 a) corresponds to $\mu = 0.4$, $\alpha = 1$, while for Figure 1 b) we have taken $\mu = 8$, $\alpha = 1$. The values of the integral in (\ref{['coso1']}) are $-9.008...$ for Figure 1 a), and $+10.39...$ for Figure 1 b).